Problem: Rewrite as a simplified fraction. ${0.\overline{57} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 57.5757...\\ 1x &= 0.5757...\end{align*}}$ Subtracting the two equations, we have: ${99x = 57}$ ${x = \dfrac{57}{99}} $ ${x = \dfrac{19}{33}} $